The Intrinsic Quantum Nature of Nash Equilibrium Mixtures

Every undergraduate textbook in game theory has a chapter discussing the difficulty to interpret the mixed Nash equilibrium strategies. Unlike the usual suggested interpretations made in those textbooks, here we prove that these randomised strategies neither imply that players use some coin flips to make their decisions, nor that the mixtures represent the uncertainty of each player about the others' actions.Instead, the paper demonstrates a fundamental connection between the Nash equilibrium 'randomised' or 'mixed' strategies of classical game theory and the pure quantum states of quantum theory in physics. This link has some key consequences for the meaning of randomised strategies:In the main theorem, I prove that in every mixed Nash equilibrium, each player state of knowledge about his/her own future rational choices is represented by a pure quantum state. This indicates that prior making his/her actual choice, each player must be in a quantum superposition over her/his possible rational choices (in the support of his probability measure). This result notably permits to show that the famous 'indifference condition' that must be satisfied by each player in an equilibrium is actually the condition that ensures each player is in a 'rational epistemic state of ignorance' about her/his own future choice of an action

The improbable transmission of Trypanosoma cruzi to human: the missing link in the dynamics and control of Chagas disease

Chagas disease has a major impact on human health in Latin America and is becoming of global concern due to international migrations. Trypanosoma cruzi, the etiological agent of the disease, is one of the rare human parasites transmitted by the feces of its vector, as it is unable to reach the salivary gland of the insect. This stercorarian transmission is notoriously poorly understood, despite its crucial role in the ecology and evolution of the pathogen and the disease. The objective of this study was to quantify the probability of T. cruzi vectorial transmission to humans, and to use such an estimate to predict human prevalence from entomological data. We developed several models of T. cruzi transmission to estimate the probability of transmission from vector to host. Using datasets from the literature, we estimated the probability of transmission per contact with an infected triatomine to be 5.8x10(-4) (95%CI: [2.6; 11.0] x 10(-4)). This estimate was consistent across triatomine species, robust to variations in other parameters, and corresponded to 900-4,000 contacts per case. Our models subsequently allowed predicting human prevalence from vector abundance and infection rate in 7/10 independent datasets covering various triatomine species and epidemiological situations. This low probability of T. cruzi transmission reflected well the complex and unlikely mechanism of transmission via insect feces, and allowed predicting human prevalence from basic entomological data. Although a proof of principle study would now be valuable to validate our models' predictive ability in an even broader range of entomological and ecological settings, our quantitative estimate could allow switching the evaluation of disease risk and vector control program from purely entomological indexes to parasitological measures, as commonly done for other major vector borne diseases. This might lead to different quantitative perspectives as these indexes are well known not to be proportional one to another

Traces possibles d'actions humaines sur des os fossiles du gisement d'« Homo Heidelbergensis »?

Pelosse J. L. Traces possibles d'actions humaines sur des os fossiles du gisement d'« Homo Heidelbergensis »?. In: Bulletin de l'Association française pour l'étude du quaternaire, vol. 3, n°4, 1966. pp. 247-250